Appendix 4: The Fall of the Fifth Force

In this episode we will examine a case of the refutation of a
hypothesis, but only after a disagreement between experimental results
was resolved. The “Fifth Force” was a proposed modification of Newton’s
Law of Universal Gravitation. The initial experiments gave conflicting
results: one supported the existence of the Fifth Force whereas the
other regued against it. After numerous repetitions of the experiment,
the discord was resolved and a consensus reached that the Fifth Force
Did not exist. A reanalysis of the original Eötvös
experiment[1]
by Fischbach
and his collaborators (1986) had shown a suggestive deviation
from the law of gravity. The Fifth Force, in contrast to the famous
Galileo experiment, depended on the composition of the objects. Thus,
the Fifth Force between a copper mass and an aluminum mass would differ
from that between a copper mass and a lead mass. Fischbach and
collaborators also suggested modifying the gravitational potential
between two masses from

\[
V = - \frac{G m_1 m_2 }{r}
\]

to

\[
V = - \frac{G m_1 m_2 }{r} [1 + \alpha e^{-r/\lambda}],
\]

where the second term gives the Fifth Force with strength \(\alpha\)
and range \(\lambda\). The reanalysis also suggested that \(\alpha\) was
approximately 0.01 and \(\lambda\) was approximately 100m. (For details of
this episode see (Franklin 1993)).

Figure 8.
Schematic diagram of the differential accelerometer used
in Thieberger’s experiment. A precisely balanced hollow copper sphere
(a) floats in a copper-lined tank (b) filled with distilled water (c).
The sphere can be viewed through windows (d) and (e) by means of a
television camera (f). The multiple-pane window (e) is provided with a
transparent x-y coordinate grid for position determination on top with
a fine copper mesh (g) on the bottom. The sphere is illuminated for one
second per hour by four lamps (h) provided with infrared filters (i).
Constant temperature is maintained by mea ns of a thermostatically
controlled copper shield (j) surrounded by a wooden box lined with
Styrofoam insulation (m). The Mumetal shield (k) reduces possible
effects du e to magnetic field gradients and four circular coils (l)
are used for positioning the sphere through forces due to ac-produced
eddy currents, and for dc tests. From Thieberger (1987).

Figure 9.
Position of the center of the sphere as a function of
time. The y axis points away from the cliff. The position of the sphere
was reset at points A and B by engaging the coils shown in Figure 21.
From Thieberger (1987).

In this episode, we have a hitherto unobserved phenomenon along with
discordant experimental results. The first two experiments on the Fifth
Force gave contradictory answers. One experiment supported the
existence of the Fifth Force, whereas the other found no evidence for
it. The first experiment, that of Peter Thieberger (1987a) looked for a
composition-dependent force using a new type of experimental apparatus,
which measured the differential acceleration between copper and water.
The experiment was conducted near the edge of the Palisades cliff in
New Jersey to enhance the effect of an intermediate-range force. The
experimental apparatus is shown in Figure 8.
The horizontal acceleration of the copper sphere relative to the water
can be determined by measuring the steady-state velocity of the sphere
and applying Stokes’ law for motion in a resistive medium. Thieberger’s
results are shown in Figure 9. The sphere
clearly has a velocity, indicating the presence of a force. Thieberger
concluded, “The present results are compatible with the existence of a
medium-range, substance-dependent force” (p. 1068).

Figure 10.
Schematic view of the University of Washington torsion
pendulum experiment. The Helmholtz coils are not shown. From Stubbs et
al. (1987).

Figure 11.
Deflection signal as a function of degrees. The theoretical
curves correspond to the signal expected for alpha = 0.01 and lambda =
100m. From Raab (1987).

The second experiment, by the whimsically named Eöt-Wash group,
was also designed to look for a substance-dependent, intermediate range
force (Raab 1987; Stubbs et al. 1987). The apparatus was located on a
hillside on the University of Washington campus, in Seattle
(Figure 10). If the hill attracted the copper
and beryllium bodies differently, then the torsion pendulum would
experience a net torque. This torque could be observed by measuring
shifts in the equilibrium angle of the torsion pendulum as the pendulum
was moved relative to a fixed geophysical point. Their experimental
results are shown in Figure 11. The
theoretical curves were calculated with the assumed values of 0.01 and
100m, for the Fifth Force parameters \(\alpha\) and \(\lambda\),
respectively. These were the best values for the parameters at the
time. There is no evidence for such a Fifth Force in this
experiment.

The problem was, however, that both experiments appeared to be
carefully done, with no apparent mistakes in either experiment.
Ultimately, the discord between Thieberger’s result and that of the
Eöt-Wash group was resolved by an overwhelming preponderance of
evidence in favor of the Eöt-Wash result (The issue was actually
more complex. There were also discordant results on the distance
dependence of the Fifth Force. For details see Franklin (1993; 1995a)).
The subsequent history is an illustration of one way in which the
scientific community deals with conflicting experimental evidence.
Rather than making an immediate decision as to which were the valid
results, this seemed extremely difficult to do on methodological or
epistemological grounds, the community chose to await further
measurements and analysis before coming to any conclusion about the
evidence. The torsion-balance experiments of Eöt-Wash were
repeated by others including (Cowsik et al. 1988; Fitch, Isaila and
Palmer 1988; Adelberger 1989; Bennett 1989; Newman, Graham and Nelson
1989; Stubbs et al. 1989; Cowsik et al. 1990; Nelson, Graham and Newman
1990). These repetitions, in different locations and using different
substances, gave consistently negative results. In addition, Bizzeti
and collaborators (1989a; 1989b), using a float apparatus similar to
that of Thieberger, also obtained results showing no evidence of a
Fifth Force. There is, in fact, no explanation of either Thieberger’s
original, presumably incorrect, results. The scientific community has
chosen, I believe quite reasonably, to regard the preponderance of
negative results as
conclusive.[2]
Experiment had shown that there is
no Fifth Force.